Board game apparatus

ABSTRACT

There is provided a board game apparatus comprising a board, one or more playing pieces, and one or more dice. The board has a plurality of cells extending between a starting cell and an ending cell, the plurality of cells being sequentially numbered to define a continuous path along the cells from the starting cell to the ending cell, such that each cell bears a unique number, wherein the cells comprise active cells each bearing a mathematical operator in addition to their number, and motive cells without any mathematical operator in addition to their number.

BACKGROUND

The present invention relates to a board game apparatus, which may beused for educational purposes.

Board games are well known, and often comprise a board defining variousplaying spaces, one or more dice, and one or more playing pieces.

Board games typically aim to be entertaining, and may also educate theplayers of the board game, with new knowledge and/or skills as the gameis played.

It is an object of the invention to provide a board game apparatus thatcan be used for educational purposes, for example in schools.

SUMMARY

According to the invention, there is provided a board game apparatuscomprising a board, one or more playing pieces, and one or more dice.The board has a plurality of cells extending between a starting cell andan ending cell, the plurality of cells being sequentially numbered todefine a continuous path along the cells from the starting cell to theending cell, such that each cell bears a unique number, wherein thecells comprise active cells each bearing a mathematical operator inaddition to their number, and motive cells without any mathematicaloperator in addition to their number.

Accordingly, an object of the game may be for each player to progresstheir playing piece(s) from the starting cell to the ending cell, andthe movement of the playing piece(s) from any active cell may be definedby the mathematical operator of the active cell when applied to thenumber of the cell and/or to the number of the dice.

The board game apparatus provides an educational and entertaining game,which exercises players' mathematical skills and helps developconcentration and memory recall. The game may also require communicationbetween the players, and may teach verbal expression, patience andpersistence, and anticipation of other player's moves. Accordingly, itmay be particularly suited to use in schools.

Preferably, there are 9 different mathematical operators which aregrouped into 3 parts. These mathematical operations and groups are:

(a) Addition + ) Multiplication × ) Square X² ) Called Ascending GroupGreater Than > ) (b) Subtraction − ) Division ÷ ) Square Root {squareroot over ( )} ) Called Descending Group Less Than <, ) (c) Equal =Called Completion Group

In the Ascending group, the mathematical operations all function toprogress the playing piece towards the ending cell, where the game iswon. In the Descending group, the mathematical operations all functionto regress the playing piece back towards the starting cell, where thegame is started. In the Completion group, the Equal sign denotes the endof the game, and is applied to the ending cell. Both the mathematicaloperations on the board and the dice go hand in hand to define how theplaying pieces are moved from cell to cell.

If a player lands their playing piece on a cell having an addition orsubtraction operator, then the player is allowed to have a second go,and the number of the cell may be added or subtracted to the number thatis rolled on the dice to define which cell number the playing piece mustbe moved to.

If a player lands their playing piece on a cell having a multiplicationor division operator, then on the player's next turn, the number of thecell may be multiplied or divided by the number that is rolled on thedice, to define which cell number the playing piece must be moved to.

If a player lands their playing piece on a cell having a square orsquare root operator, then the number of the cell may be immediatelysquared or square rooted, to define which cell number the playing piecemust be moved to. Clearly, there is a need to make sure that the numberof any active cell bearing a square operator, when squared, does notequal the number of an active cell having a square root operator toprevent an endless loop.

If a player lands their playing piece on a cell having a greater than orless than operator, then on the player's next turn, the number of thecell may be compared to the number that is rolled on the dice, to definewhich cell number the playing piece must be moved to.

Each mathematical operator when operated with the number of the cellbearing that mathematical operator, and when applicable the number thatis rolled by the dice, preferably results in a number that is present onone of the cells of the board. Accordingly, the mathematical operators,the cell numbers, and the numbers on the dice should be carefullychosen.

For example, the board may have 144 cells, numbered sequentially from 1to 144 along a continuous path. Accordingly, with a six sided dice, onlycells 60 and 120 may bear a division operator since those are the onlynumbers from 1 to 144 that result in a whole number when divided by anyone of 1 to 6. All other numbers other than 60 and 120 when divided by 1to 6 by way of the dice will always result with at least one answerbeing a decimal point or fraction.

Additionally, the highest numbered cell bearing a multiplicationoperator may be cell 24, since when 24 is multiplied by 6 by way of thedice, to give 144, the playing piece will be moved to cell 144, whichdenotes the end of the game. Clearly, if a multiplication operator wasapplied to cell 25 or greater, then the result of the multiplicationwith the dice will give a result higher than 144, which is outside therange of the board.

Some certain mathematical operators may link to one another, with theexception of a Square operator to a Square Root operator. Specifically,when a playing piece is on an active cell, that playing piece may moveto another active cell if the correct dice number is thrown.

Optionally, the sum of two six-sided dice may be used to generate anumber for operation with the mathematical operator of an active cell,provided only whole numbers on the board could result from themathematical operator and dice sum.

Preferably, the board provides a continuous winding square path in theform of a spiral around a central point.

Optionally, each player may be provided with two playing pieces, so thatthey can choose which playing piece they wish to move at each turn.Accordingly, the board game apparatus may comprise pairs of playingpieces, the playing pieces of each pair being identical to one another.Preferably, the board game apparatus comprises a cup for shaking thedice before throwing, and an instruction card with a set of rules forplaying the game.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described with reference to theaccompanying drawings, in which FIG. 1 shows a diagram of a boardforming part of a board game apparatus according to an embodiment of theinvention, and FIGS. 2-10 show isolated portions of the board of FIG. 1.

DETAILED DESCRIPTION

First referring to FIG. 1, there is shown a diagram of a board which hasa 12×12 grid of 144 cells, numbered from cell 1 at the start to cell 144at the end in a square spiral formation with cell 144 at the centre.Cell 1 is the starting cell and cell 144 is the ending cell, and thenumbers define a continuous path along the cells that inwardly spiralsfrom the starting cell 1 at an edge of the board to the ending cell 144at the centre of the board. In this embodiment the board has a whiteborder extending around the periphery of the cells. It also hasmathematical operators displayed on certain cells, which are referred toas active cells. The board forms part of a board game apparatus thatalso comprises four six-sided dice, and four pairs of playing pieces.The pairs of playing pieces are assigned to respective players, and theplaying pieces of each pair are identical to one another, so there arefour different types of playing piece, one type for each player. Eachplaying piece fits within one cell when placed upon the board, andpurely acts as a marker for which cell each player is currently on. Thedices and the playing pieces are conventional, and so will not bedescribed in any further detail herein.

There are 34 mathematical operators on the cells of the board of FIG. 1in total. These mathematical operators are:

Addition + Subtraction − Multiplication × Division ÷ Square x² SquareRoot {square root over ( )} Greater Than > Less Than < Equal =

The Ascending Mathematical Operation

There are 4 ascending mathematical operators which are:

Addition + Multiplication × Square x² Greater Than >

These symbols are placed on specific cells on the board of FIG. 1 whichare as follows:

Addition + Multiplication × Square x² Greater Than > 30 4 9 43 40 20 1155 47 24 62 74 72 92 99 107 117 138

There are 9 Additions, 3 Multiplications, 2 Squares, and 4 GreaterThans, which totals up to 18 Ascending Mathematical operators.

The Descending Mathematical Operation

There are 4 descending mathematical operators which are:

Subtraction − Division ÷ Square Root {square root over ( )} Less ThanThan <

These symbols are placed on specific cells on the board of FIG. 1 whichare as follows:

Subtraction − Division ÷ Square Root {square root over ( )} Less Than <48 60 36 17 66 120 64 71 113 100 88 133 126 142 136

There are 5 Subtractions, 2 Divisions, 3 Square Roots, and 5 Less Thans,which totals up to 15 Descending Mathematical operators.

The Completion Mathematical Operation

The Equal=symbol denotes the end of the game which is on cell 144 ⁼. Soin total there are 34 mathematical operators placed on specific cells onthe board as described previously whilst there are 110 cells without anymathematical operators. An active cell is a cell with a mathematicaloperator. A motive cell is a cell without a mathematical operator.

Linkages Between Active Cells

The active cells are arranged on the board of FIG. 1 so that some activecells lead to other active cells. Specifically, when a playing piece ison an active cell, that playing piece may move to another active cell ifthe correct dice number is thrown. The following table shows the linksbetween the active cells of FIG. 1.

From Active Cell To Active Cell Addition + −, ÷, {square root over( )}, > Subtraction − +, ÷, {square root over ( )}, >, < Multiplication× +, −, ×, ÷, {square root over ( )}, > Division ÷ +, ×, ÷ Greater Than>+, −, ÷ Less Than < ×

For a first active cell to link to a second active cell, the secondactive cell must be placed a first number of cells from the first activecell, wherein the first number is equal to a result of a rolled numberapplied to the mathematical operator borne by the first one of theactive cells, and wherein the rolled number is a number which isrollable by one of the dice.

Applying Mathematical Operators

The different mathematical operators are applied at different points inthe game, depending on the mathematical operator, as follows.

When landing on these, the player immediately applies the mathematicaloperators and moves to the appropriate cell:

Addition + Subtraction − Square x² Square Root {square root over ( )}

When landing on these, the player remains until their following turnwhen the mathematical operators are applied:

Multiplication × Division ÷ Greater Than > Less Than <

Although not shown in FIG. 1 for clarity, each type of mathematicaloperator has a specific colour associated with it, in which its cellsare coloured, as a means of identification. The motive cells are allcoloured Grey for this particular board but for other boards can begiven other colours. For example, the colours of the cells of eachmathematical operator may be as follows:

Blue associated with Addition + Orange associated with Subtraction −Green associated with Multiplication × Grey associated with Division ÷White associated with Square x² Brown associated with Square Root{square root over ( )} Yellow associated with Greater Than > Redassociated with Less Than < Black associated with Equal =

Functions of Mathematical Operations

The Ascending Mathematical Operation Functions:

Addition + is the process when combining 2 or more numbers to get thetotal. When landing on a cell with an addition symbol, the player has asecond go and advances forward. For example, on cell 30 with an additionsymbol + illustrated as 30⁺ on FIGS. 1 and 2, the addition mathematicaloperator will be applied to dice rolls of 1 to 6 as follows:

Multiplication X is the process of adding a number to itself a certainnumber of times. When landing on a cell with a multiplication symbol,the cell becomes active on player's next turn and advances forward. Forexample on cell 20 with a multiplication symbol × illustrated as 20X onFIGS. 1 and 5, the multiplication mathematical operator will be appliedto dice rolls of 1 to 6 as follows:

Alternatively, the multiplication mathematical operator could be appliedas follows, according to a set of rules called Standard Version 5:

Square X² is the number that results from multiplying a number byitself. When landing on a cell with a square symbol, the cell becomesactive immediately and the player moves forward to its appropriatecell/answer e.g. on Cell 11 with a square symbol ×² illustrated as11^(×2) which is an active ascending cell on FIGS. 1 and 8, the playermoves forward to cell 121 which is a motive cell.

$\begin{matrix}{11^{x\; 2} = {11 \times 11}} \\{= {121\mspace{11mu} \left( {{Cell}\mspace{14mu} 121} \right)}}\end{matrix}$

Greater Than > is when one number is bigger than another by how much(difference). When landing on a cell with a greater than operator thecell becomes active on the player's next turn and advances forward. Forexample, on Cell 55 with a greater than operator > illustrated as 55^(>)on FIGS. 1 and 4, the greater than operator will be applied to dicerolls of 1 to 6 as follows:

The Descending Mathematical Operation Functions

Subtraction − is the process of finding the difference between twonumbers. When landing on a cell with a subtraction symbol the player hasa second go and advances backwards. For example on Cell 48 with asubtraction operator—illustrated as 48⁻ on FIGS. 1 and 3, thesubtraction operator will be applied to dice rolls of 1 to 6 as follows:

Division ÷ is the process of calculating how many times one quantity iscontained in another. When landing on a cell with a division symbol thecell becomes active on player's next turn and retreats backwards. Forexample on cell 120 with a division symbol ÷ illustrated as 120^(÷) onFIGS. 1 and 6, the division operator will be applied to dice rolls of 1to 6 as follows:

Alternatively, the division mathematical operator could be applied asfollows, according to the set of rules called Standard Version 5:

Square Root √{square root over ( )} is a number that can be multipliedby itself to produce a given number. When landing on a cell with asquare root symbol, the cell becomes active immediately and the playermoves backwards to its appropriate cell/answer. For example on cell 64with a square root symbol √{square root over ( )} illustrated as√{square root over ( )} 64 on FIGS. 1 and 9, the player moves backwardsto cell 8.

$\begin{matrix}{{\sqrt{\;}64} = {8 \times 8}} \\{= {8\mspace{14mu} {being}\mspace{14mu} {the}\mspace{14mu} {answer}\mspace{11mu} \left( {{cell}\mspace{14mu} 8} \right)}}\end{matrix}$

Less Than < is when one number is smaller than another by how much(difference). When landing on a cell with a less than symbol, the cellbecomes active on the player's next turn. For example on Cell 71 with aless than symbol < illustrated as <71 on FIGS. 1 and 7, the less thanoperator will be applied to dice rolls of 1 to 6 as follows:

Method of Play

To start the game, the player who rolls the lowest or highest number onthe dice commences the game depending on which game version is beingplayed.

The game direction is in counter clockwise.

Commence Play

The player with the lowest or highest number on the dice depending onwhich game version is played rolls the dice again to show the number ofcells that the player has to move initially on the board. The playermoves playing piece on the appropriate cell. For example Player A whostarts the game rolls 2 on the dice and then moves to Cell 2 on theboard. Now it is Player B's turn to roll and rolls 6 on the dice andthen moves to Cell 6 on the board. This example is based on a 2 playergame.

Continue Play

On the next turn, the player rolls the dice again to show number ofcells that the player has to move on the board. For example, Player Arolls 3 on the dice and then moves to cell 5 on the board. Whilst,Player B rolls 4 on the dice and then moves to cell 10 on the board.

However, if player lands on an active cell certain actions must betaken:

Addition + this means player has second go and move playing pieceforward 1 of 6 ways, depending on the dice number that has been thrown.

Subtraction − this means player has second go and move playing piecebackwards 1 of 6 ways depending on the dice number that has been thrown.

Multiplication × this means player moves forward 1 of 6 ways dependingon the dice number that is thrown on player's next turn.

Division ÷ this means player moves backwards 1 of 6 ways depending onthe dice number that is thrown on player's next turn.

Square X² this means player moves their playing piece forwardimmediately to the appropriate answer/cell when landed upon.

Square Root √{square root over ( )} this means player moves playingpiece backwards immediately to the appropriate answer/cell when landedupon.

Greater Than > this means player moves playing piece forward 1 of 6 waysdepending on the dice number that is thrown on player's next turn.

Less Than < this means player moves playing piece backwards 1 of 6 waysdepending on the dice number that is thrown on player's next turn.

Complete the Game

The first player to reach cell 144= (central point) is the winner butthe player must roll the exact number on the dice to land on cell 144which has the Equal = symbol resulting in the end of the game.

Variations of Gameplay

There are 5 different methods of play which are listed as:

1. Standard version 1

2. Standard version 2

3. Standard version 3

4. Standard version 4

5. Standard version 5

Standard Version 1

This game version is played with 2-4 players, each player has oneplaying piece and one dice is used.

To Start the Game

The player who rolls the highest number on the dice commences the game.When a playing piece lands on an active cell the following actionsapply:

Movement of Playing Piece when on Active Cell

Addition + symbol, player has a second go and advances playing pieceforward depending on the dice roll. For example on cell 40 with anaddition symbol + illustrated as 40+ on FIG. 1, the addition operatorwill be applied to dice rolls of 1 to 6 as follows:

Subtraction − symbol, player has a second go and retreats backwardsdepending on the dice roll. For example on Cell 66 with a subtractionsymbol − illustrated as 66⁻ on FIGS. 1, the subtraction operator will beapplied to dice rolls of 1 to 6 as follows:

Multiplication × symbol, when player lands on this symbol the cell withthis symbol becomes active/activated on player's next turn. For exampleon cell 4 with a multiplication symbol X illustrated as 4× on FIGS. 1and 5, the multiplication operator will be applied to dice rolls of 1 to6 as follows:

Division ÷ symbol, when the player lands on this symbol the cell withthis symbol becomes active/activated on player's next turn. For exampleon cell 60 with division symbol ÷ illustrated as 60÷ on FIG. 1, thedivision operator will be applied to dice rolls of 1 to 6 as follows:

Square X² symbol, when player lands on this symbol the cell becomesactive immediately and player moves forward to its appropriatecell/answer. For example on cell 9 with a square symbol x² illustratedas 9^(x2) on FIG. 1, this takes player to cell 81.

$\begin{matrix}{9^{x\; 2} = {9 \times 9}} \\{= {81\mspace{11mu} {\left( {{cell}\mspace{14mu} 81} \right).}}}\end{matrix}$

Square Root √{square root over ( )} symbol, when the player lands onthis symbol the cell becomes active immediately and player movesbackwards to its appropriate cell/answer. For example on cell 100 with asquare root symbol √{square root over ( )} illustrated as √{square rootover ( )} 100 on FIGS. 1 and 7, this takes player to cell 10.

$\begin{matrix}{{\sqrt{\;}100} = {10 \times 10}} \\{= {10\mspace{14mu} {being}\mspace{14mu} {the}\mspace{14mu} {answer}\mspace{11mu} \left( {{cell}\mspace{14mu} 10} \right)}}\end{matrix}$

Greater Than > symbol, when player lands on this symbol the cell withthis symbol becomes active/activated on player's next turn. For exampleon cell 72 with greater than symbol > illustrated as 72^(>) on FIG. 1,the greater than operator will be applied to dice rolls of 1 to 6 asfollows:

Less Than < Symbol, when player lands on this symbol the cell with thissymbol becomes active/activated on player's next turn. For example oncell 88 with less than symbol illustrated as <88 on FIGS. 1 and 4, theless than operator will be applied to dice rolls of 1 to 6 as follows:

To End Game

The player who reaches cell 144 first wins the game.

Standard Version 2

This game version is played with 2-4 players using 2 dices and eachplayer has 2 playing pieces.

To Start the Game

The player who rolls the lowest number on the dice commences the game.Players must move both of their playing pieces when the 2 dices arerolled. For example player rolls Dice 4 and Dice 6, player then movesone playing piece to Cell 4 ^(×) on the board and moves the otherplaying piece to Cell 6 on the board.

Terms of the Game

Displace—Is when a playing piece lands on a motive cell occupied by anopponent playing piece(s) and sends that playing piece out of the game.

For example, if player A has one or two playing pieces on a motive cellsuch as Cell 7 and opponent player B was on Cell 2 and Cell 10 nowplayer B's turn and rolls Dice 2 and Dice 5, moves 2 steps from Cell 10to Cell 12 (using dice 2) with one playing piece and moves other playingpiece 5 steps from cell 2 to Cell 7 (using dice 5). The latter movementdisplaces player A's playing pieces and sends (locks) them out of thegame.

Locked Out—Is when a playing piece that has been displaced is out of thegame and needs to roll a 6 on the dice to enter back into the game onCell 6.

Example 1: If a player's playing piece is locked out and the otherplaying piece is in play on Cell 7 and a set of 2 dices is rolled, say 3and 6 the locked out playing piece must come into play on cell 6 (dice 6used) and the other player piece therefore utilises dice 3 to move 3steps from cell 7 to cell 10.

NOTE: When dice 6 is rolled and a playing piece is locked out this piecemust always come into play on cell 6.

Example 2: If one playing piece is locked out and the other playingpiece can land on an active cell with at least one of the dices, thatplaying piece must land on it using only that dice to move.

-   -   One playing piece locked out and    -   other playing piece on cell 12 and    -   Dice roll 4 and 5    -   Playing piece on cell 12 can't move to cell 16 (dice 4 used) but        must move to cell <17 (dice 5 used) as explained.

The only exception is if your opponent is before the active cell you candisplace their playing piece to eliminate the threat. But if theopponent is after the active cell then you have to move to the activecell.

At a standstill—Is when a playing piece is unable to move due to nothaving the right number on the dice to move to cell 144 ⁼ which denotesthe end of game. From cell 139 to cell 143 is called the standstillzone, except for cell 142 ⁻.

For example, if a player has one playing piece at a standstill and theother playing piece is not and the player rolls 2 sets of dices 4 and 5the playing piece not at a standstill chooses one dice to move. Thisplaying piece is not forced to move to an active cell even if one of thedices suggests so.

-   -   One playing piece at a standstill on cell 143 and other playing        piece on cell 12 and Dice roll 4 and 5.    -   Playing piece on cell 12 is not forced to move to cell <17 (dice        5 used) but can move to cell 16 (dice 4) instead.

To Enter Game When Locked Out

If a player has one or two playing pieces locked out then each playingpieces needs a solid 6 on the dice(s) separately to enter back into thegame on cell 6.

-   -   Both playing pieces locked out    -   Dice roll 1 and 6    -   Then only one playing piece enters into game on Cell 6    -   The other playing piece remains locked out until a solid 6 is        rolled next time on player's next turn.

NOTE If a double 6 is rolled then both playing pieces enter on cell 6together.

Movement of Playing Piece when on Active Cell

If player lands 2 playing pieces on same or different cells ofmultiplication ×, division ÷, greater than > Less than < the followingrules apply:

When on Same Active Cell

One playing piece moves according to one dice to a particular cell andthe other playing piece moves according to the other dice to aparticular cell.

When on Different Active Cell

One playing piece moves according to one dice to a particular cell andthe other playing piece moves according to the other dice to aparticular cell or vice versa.

If player lands 2 playing pieces on same or different cells of square X²or Square root √{square root over ( )} the following rules apply:

When on Same Active Cell

Both playing pieces moves to particular cell regardless on dice rolls,once playing pieces lands on cell with square or square root symbol.

When on Different Active Cell

Both playing pieces moves to their own particular cell regardless ondice rolls, once playing pieces lands on cell with square or square rootsymbol.

If player lands 2 playing pieces on same or different cells ofaddition + or subtraction − the following rules apply:

When on Same Active Cell

One playing pieces moves according to one dice to a particular cell andthe other playing piece moves according to the other dice to aparticular cell.

When on Different Active Cell

Each playing piece has a second go and rolls the dices and movesaccordingly.

NOTE: If only one playing piece lands on a cell with an addition orsubtraction operation, then it has a second go.

End of Game for Playing Piece

Each player has 2 playing pieces, when one playing piece gets to cell144 ⁼ which denotes end of game for that playing piece, it is removedfrom the game along with one dice. Now that player has one playing pieceleft and only rolls one dice and not 2 sets of dices.

To End Game

If playing piece is on cell 139-143 except for cell 142 ⁻ and playerrolls any digit on dices from 1-5 except for 2, player has to moveplaying piece to cell 144 ⁼ to end that playing piece game. This takesprecedence over the other playing piece, when one of the dice digits isabove the other dice digit to get out to cell 144 ⁼.

Example 1: One playing piece on cell 139

-   -   the other playing piece on cell 80    -   Dice roll 5 and 6    -   Playing piece on cell 139 moves 5 steps (dice 5 used) to cell        144 ⁼    -   And other playing piece moves 6 steps (dice 6 used) from cell 80        to cell 86.

The only way when playing piece does not go out to cell 144 ⁼ is whenone of the dice digits is below the other dice digit to get out to cell144 ⁼

Example 2: One playing piece on cell 139

-   -   the other playing piece on cell 80    -   Dice roll 4 and 5    -   Instead of moving 5 steps (dice 5) from cell 139 to cell 144 ⁼    -   It can move 4 steps (dice 4) from cell 139 to cell 143 and the        other playing piece moves 5 steps (dice 5) from cell 80 to Cell        85.

To End Game

On Cell Steps End of Game 139 needs 5 (dice 5) to Cell 144= 140 needs 4(dice 4) to Cell 144= 141 needs 3 (dice 3) to Cell 144= 143 needs 1(dice 1) to Cell 144=

Standard Version 3

This game version is played with 2-4 players using 2 sets of dices andeach player has 2 playing pieces.

To Start the Game

The player who rolls the lowest number on the dice commences the game.

Movement of Playing Piece

There are 2 types of movement and player can move either way.

(a) Move both playing pieces when the 2 dices are rolled, each playingpiece moves according to one dice.

(b) Move one playing piece by utilising the 2 dices rolled.

Terms of the Game

Displace

For example. If player rolls 2 sets of dices and uses one dice todisplace the opponent, the second dice can be used to move on from thepoint of displacement.

-   -   Player A on cell 3.    -   Opponent B on cell 8.    -   Player A dice roll 4 and 5.    -   Player A moves playing piece from cell 3 to cell 8 using dice 5        and displaces opponent B and now player A continues movement        from cell 8 to cell 12 using dice 4.

Locked Out

If one playing piece is locked out and the other playing piece can landon an active cell with at least one of the dice, that playing piece mustland on it and uses the second dice to complete move.

Example: One playing piece locked out and other playing piece on cell124.

-   -   Dice roll 2 and 4.    -   Move playing piece from cell 124 to cell ^(<) 126 (dice 2) and        then retreats to cell 4 ^(X) (dice 4).

At a Standstill

For example, if a player has one playing piece at a standstill and theother playing piece is not and the player rolls 2 sets of dices 4 and 5the playing piece not at a standstill uses both dices to move.

This playing piece is not forced to move to an active cell if the diceroll suggests so.

Example: One playing piece at a standstill on cell 143 and other playingpiece

-   -   on cell 12 and    -   Dice roll 4 and 5    -   Playing piece on cell 12 is not forced to move to cell <17        (dice 5) but    -   can move to cell 21 (4+5=9 steps) instead by moving 1^(st) with        dice 4 (cell 16) and then dice 5 from cell 16 to cell 21.

Blocking the Path—Is when a player's 2 playing pieces are on the samemotive cell this creates a ‘block’ whereby the opponent cannot land onthat cell or pass that cell therefore the opponent has to remain whereit is.

Example 1: Player A has 2 playing pieces on cell 10 and

-   -   Player B one playing piece is locked out and the other playing        piece is on cell 8.    -   Dice roll 2 and 5 for player B.    -   Player B can't move (2+5=7 steps) from cell 8 to cell 15 as the        path is blocked on cell 10 therefore has to remain on cell 8.

The only time when player can move is when the dice roll is below thecell which is blocked.

Example 2: Player A has 2 playing pieces on cell 10

-   -   Player B one playing piece on cell 2 and the other playing piece        on cell 5    -   Dice roll 2 and 5 for Player B    -   Therefore can move playing piece from cell 2 to cell 7 (dice 5)        and move other playing piece from cell 5 to cell 7 (dice 2).

Example 3: Player A has 2 playing pieces on cell 10.

-   -   Player B one playing piece is on cell 4 ^(×) and the other        playing piece is on cell 8.    -   Dice roll 4 and 5 for Player B.    -   Player B can't move either playing piece as the steps to move    -   One playing piece or both playing pieces goes beyond the blocked        path (cell 10).    -   Player B's playing piece on cell 4 ^(×) will either move to cell        16 (cell 4×dice 4=cell 16) or to cell 20 ^(×) (cell 4×dice        5=cell 20 ^(×)) or to cell 36 (dice 4+dice 5=9×cell 4=cell 36)        and player B's other playing piece on cell 8 will either move to        cell 12 (dice 4) or to cell 13 (dice 5) or to cell ^(<) 17 (dice        4+dice 5=9 steps).

In all cases playing pieces can't move and must remain where they are asthe path is blocked on cell 10.

Remainders—is when one playing piece is moved utilising both sets ofdices, one dice by way of steps is used to move playing piece onto anactive addition or subtraction operator cell and has a second go and theother dice from the set of dice is used to complete the movement.Remainders works on cells with addition and subtraction only.

Example: One playing piece on cell 115

-   -   Dice roll 2 and 3    -   Moving playing piece from cell 115 to cell 117 ⁺ (dice 2)    -   Carry the remainder (dice 3)    -   Now has a second go on Cell 117 ⁺ and    -   Dice roll again 1 and 2 and move from cell 117+ to cell 120 ^(÷)        (1+2=3 steps)    -   And then utilises the remainder 3 to divide 120 (^(120/3))    -   And then retreats to cell 40+.

NOTE: There is only one remainder, never more than one remainder.

Locked Out and At a Standstill

If one playing piece is locked out and the other playing piece is at astandstill such as on cell 143 and dice roll 1 and 2, the playing pieceon cell 143 still can't move as both dices have to be used.

If one playing piece is at a standstill such as on cell 143 and theother playing piece is locked out and dice roll 2 and 6, the playingpiece locked out can use both dices to move first to cell 6 (dice 6) andthen to cell 8 (dice 2).

Also playing piece on cell 95 and dice roll 3 and 4, moves playing piecefrom cell 95 to cell 99 ⁺ by 4 steps (dice 4) and carries the remainder3 (dice 3) as player has a second go and rolls dice 2 and 4 then movesfrom cell 99 ⁺ to cell 105 (2+4=6 steps) but uses the carry 3 remainderto move to cell 108 (dice 3−the remainder) to complete move.

NOTE: If player rolls a second go and it lands on an active cell theremainder is used to complete the overall move.

Also, if one playing piece is locked out and the other is on a cell <126and dice roll is a combination of 6, there are 2 possible ways to play:

(a) The playing piece locked out comes in on cell 6 and the otherplaying piece on cell <126 becomes now deactivated and therefore remainson it. OR

(b) Retreat back to cell 6 from cell <126 and the other playing piecetherefore remains locked out.

To Enter Game when Locked Out

This is the same as in Standard Version 2, except that there is also asecond way on how to enter game and this is by way of combination of 6on the dices for one playing piece.

Example: One playing piece locked out

-   -   Dice roll 2 and 4    -   This playing piece enters into game on cell 6 (dice 2+4=6)

NOTE: Combination of 6—Dices 1 and 5=6

-   -   Dices 2 and 4=6    -   Dices 3 and 3=6

NOTE: When a 6 or a combination of 6 on the dices are rolled the playingpiece locked out is not compulsory to come into play on cell 6. Theplaying piece already in play can utilise dices to move.

Movement of Playing Piece when on Active Cell

If both playing pieces are moved and one playing piece lands on anactive cell (ascending or descending), the cell gets activated onplayer's next turn. But if moving one playing piece and it lands on anactive cell using one dice, the cell becomes activated straight-awaywith the other dice.

Example: Playing piece on cell 19

-   -   Dice roll 1 and 4    -   move playing piece from cell 19 to cell 20 ^(×) (dice 1)    -   now playing piece on cell 20^(×) activated straightaway moves        from cell 20 ^(×) to cell 80 by using dice 4 (20×4=80).

If playing piece on a cell with less than and the other playing piece iseither at a standstill or locked out and dice roll is any double digitexcept for digit 4, the playing piece gets locked out the game.

Example: Playing piece on cell <17

-   -   Dice roll double 5    -   Move playing piece to cell 5 (dice 5) and then moves backwards 5        steps (dice 5) to out of the game.

But if

-   -   Dice roll 2 and 5    -   Moves playing piece from cell <17 to cell 5 (dice 5)    -   And retreats back again to cell 3 (dice 2)

NOTE: If player moves to cell 2 then automatically playing piece is outof game as 5 steps will go beyond game. This is a penalty. OR add bothdices up to be 2+5=7 therefore retreat to cell 7.

NOTE: When playing piece lands on cell 138 ⁺

-   -   Now has a second go to cell 138 ⁺ and    -   Dice roll again 4 and 6 and move from cell 138 ⁺ to cell 144 ⁼        (dice 6) and then bounces back to cell 140 (dice 4).

Deactivated

Is a cell which becomes deactivated when a playing piece which landed onit still remains after utilising the dice roll. Digit one on the dice isthe deactivator.

Example Playing piece on cell 120 ^(÷)

-   -   Other playing piece on cell 12    -   Dice roll 1 and 2    -   Playing piece on 120 ^(÷) uses dice 1 to remain (120÷1=120) and        Other playing piece moves from cell 12 to cell 14 (dice 2).

OR

-   -   Player A on cell 120 ^(÷)    -   Player B on cell 120 ^(÷)    -   Player A dice roll 1 and 2 and    -   Uses dice 1 to remain on cell 120 ^(÷) and    -   Player B dice roll 1 and 5 and uses dice 1 to remain on cell 120        ^(÷) but this action will displace Player A playing piece and        lock it out of the game.

NOTE: Deactivated works on cells with multiplication and divisionoperations.

Standard Version 4

This game version is played with 2-4 players using 2-4 dices dependingon the amount of players. Each player has only one playing piece.

Eg if 2 players playing therefore 2 dices are used

-   -   if 3 players playing therefore 3 dices are used    -   if 4 players playing therefore 4 dices are used

To Start the Game

The player who rolls the highest number on the dice commences the game.This player rolls set of dices again and chooses one dice to moveplaying piece on a particular cell on the board. Then next playerchooses one dice out of the remaining set of dices left to move playingpiece on a cell on the board. This happens until the last player has thelast dice remaining to move onto the board.

And now it's the next player after the first turn to roll the set ofdices and the process is the same as mentioned above. Cycle continuesuntil the game is ended and only one player is left.

Terms of the Game

Displace At a standstill Locked Out Pass the roll

Pass the roll—Is when a player rolls their turn of the dices and cannotmove playing piece due to it being locked out or at a standstill. Thenext player in the counter clockwise position takes the player's rolland adds towards theirs and the remaining other dices are for the otherplayers to choose from. If this player cannot move also then it goes tothe next player, therefore that player has 3 dices to use if in a 3player game.

Example: Player A locked Out—2 player game

-   -   Player B on cell 10    -   Player A dice roll 4 and 5 but needs a 6 on dice to enter game    -   Therefore remains locked out.    -   Player B now takes both dices 4 and 5 to move    -   Moves from cell 10 to cell 19 (4+5=9 steps)    -   This is called Pass the roll.

Movement of Playing Piece when on Active Cell

All different playing pieces can land on same active cells. But if on anactive cell and one rolls double digits from 2-6, if one can land onanother active cell both playing pieces can stay on it.

Example: Player A on cell 4 ^(×)

-   -   Player B on cell 4 ^(×)    -   Player A dice roll double 6    -   Player A moves playing piece from cell 4 ^(×) to cell 24 ^(×)        (4×6=24) and    -   Player B moves playing piece from cell 4 ^(×) to cell 24 ^(×)        (4×6=24)

But if one lands on a motive cell from an active cell with double digitsthen the first player to move gets displaced and locked out.

Example: Player A on cell 4 ^(×)

-   -   Player B on cell 4 ^(×)    -   Player A dice roll double 2    -   Player A moves playing piece from cell 4 ^(×) to cell 8 (4×2=8)        and    -   Player B moves playing piece from cell 4 ^(×) to cell 8 (4×2=8)        and displaces player A playing piece and is locked out.

Also if different opposing playing pieces are on the same active cellwith a multiplication × or division ÷ symbol and one rolls a double 1then that player's marker remains on that cell but now the cell hasbecome deactivated for that marker. Likewise the opponent player'smarker remains on that cell too and displaces and locks out the opposingmarker. The cell is no longer active on player's next turn as the cellhas already been activated.

Example: Player A on cell 4 ^(×)

-   -   Player B on cell 4 ^(×)    -   Player A dice roll double 1    -   Player A playing piece remains on cell 4 ^(×) (4×1=4 cell)    -   Player B playing piece remains on cell 4 ^(×) (4×1=4 cell) and        displaces player A playing piece and is locked out.

When a playing piece is on a standstill zone cell (Cell 139-143 except142) and it cannot move it passes the roll to the opponent player. Nowif the opponent player's playing piece is on an active cell and whetherit retreats backwards or advances forwards onto another active cell, thesecond dice is used straightaway to activate that cell.

Example: Player A on cell 141

-   -   Player B on cell 120 ^(÷)    -   Player A dice roll 4 and 6 and    -   Player A playing piece cannot move therefore pass the roll    -   Player B playing piece moves from cell 120 ^(÷) to cell 20 ^(×)        (120÷6=20) and from cell 20 ^(×) moves to cell 80 (20×4=80).

Second Go's

-   -   All players must finish moving playing pieces across the board        before the player which landed on a second go cell (cells with        addition or subtraction operations) has a second chance to roll        the dices again and add them up to move.    -   If opposing players land on a second go cell, each player has a        second go to roll the dices again to move their playing piece.    -   Before a player's turn to roll the dices and their playing piece        landed on a second go cell, this player now has 2 turns to roll        the dices, the first being to roll a second go (add all dices        and move) and then the second being to roll normal turn and        chooses best dice to move.    -   Also when on a second go cell one can split dice moves; use one        dice to land on an active cell except for second go cells and        use the other dice to complete move.

Example: Player A on cell 40 ⁺

-   -   Dice roll 1 and 3 (second go turn)    -   Player A moves playing piece from on cell 40 ⁺ to    -   Cell 43 ^(>) (dice 3 used)    -   And moves from cell 43 ^(>) to cell 85 (dice 1 used).    -   Also when on a second go cell and player rolls dices and move        playing piece, one can only land on another second go when all        dices have been used to move.

Example: Player on cell 142 ⁻

-   -   Dice roll 4 and 5    -   move playing piece from cell 142 ⁻ to cell 133 ⁻ (4+5=9)    -   Dice roll 1 and 2, move playing piece from cell 133 ⁻ to cell        130 (1+2=3)    -   When playing piece lands on cell 138 ⁺, this is the only cell        when dice roll can exceed the board but can bounce back in.

To Prevent An Opponent from Moving when it is at a Standstill

If a player wants to prevent an opponent from moving then the player hasto take the dice which the opponent can use to move first and use seconddice to complete movement.

Example: Player A on cell 143

-   -   Player B on cell 52    -   Player B's turn roll dices 1 and 6    -   To prevent player A winning to cell 144 ⁼    -   Player B will use dice 1 to move from cell 52 to cell 53 first    -   And then use dice 6 to move from cell 53 to cell 59 to complete        move.

To Enter Game when Locked Out

So long as dice 6 remains in play any number of players can enter backinto the game on any cell corresponding to the dices.

Example: For a 4 player game

-   -   Player A already in play on cell 10    -   Player B already in play on Cell 49 But    -   Player's C and D are locked out    -   Dice roll 4, 3, 6, 1    -   Player A uses dice 4 to move 4 steps to cell 14    -   Player B uses dice 1 to move 1 step to cell 50    -   Player C uses dice 6 to move 6 steps to cell 6    -   Player D remains locked out as dice 6 is no longer in play        therefore has to pass the roll to player A who moves 3 steps        (dice 3) to cell <17.

To Tie or Draw

For this version there is a possibility of a draw or tie break.

Example: Player A on cell 140

Player B on cell 143

Player B's dice roll 1 and 4

-   -   Therefore Player B uses dice 1 to move to Cell 144 ⁼ and Player        A uses dice 4 to move to cell 144 ⁼.

To End Game

When a player reaches to cell 144 ⁼ that player has won the game asfirst place and therefore one dice is removed from the game to allow theother remaining players to continue play.

Example: 4 Player Game

-   -   Player A on cell 144 ⁼ first therefore one dice is removed    -   Now 3 dices are used instead of 4 for the 3 other remaining        players.    -   This carries on until one player left in the game.

2 Player Game for Standard Version 4 with 2 Playing Pieces Each Using 4Dices

This is a subversion of Standard Version 4 whereby each player has 2playing pieces. A player rolls 4 sets of dices but chooses 2 dices firstto move and then the opponent player chooses the remaining other 2 dicesto move. Now it's the other player's turn to roll 4 sets of dices andchooses 2 dices most suitable to move whilst the other player has theremaining 2 dices to move.

Standard Version 5

This version is similar to Standard Version 1. The difference is withthe multiplication and division operations and how it operates. Thisgame version is played with 2-4 players each player has one playingpiece and one dice is used to play.

To Start the Game

The player who rolls the highest number on the dice commences the game.

Movement of Playing Piece when on Active Cell

When playing piece lands on an active cell the following actions apply:

For Addition + Square X² Greater Than > Subtraction − Square Root{square root over ( )} Less Than <

Same rules apply as Standard Version 1. Only multiplication × anddivision ÷ have a different rules of play to Standard Version 1. This islisted as follows:

Multiplication × Symbol, when player lands on this symbol the cell withthis symbol becomes active/activated on player's next turn. For exampleon cell 4 with multiplication symbol × illustrated as 4^(×) when rolldice 1 to 6 will be:

Division ÷ Symbol, when player lands on this symbol the cell with thissymbol becomes active/activated on player's next turn. For example oncell 60 with division symbol ÷ illustrated as 60^(÷) when roll dice 1 to6 will be:

To End Game

The player who reaches cell 144 first becomes the winner.

Duration of Game

On average game play is between 5-20 minutes.

-   -   Further variations on the rules may also be implemented, along        with variations to the numbering of the board, within the scope        of any one of the appended claims.

1. A board game apparatus, comprising a board, one or more playingpieces, and one or more dice, wherein the board has a plurality of cellsextending between a starting cell and an ending cell, the plurality ofcells being sequentially numbered to define a continuous path along thecells from the starting cell to the ending cell, such that each cellbears a unique number, wherein the cells comprise active cells eachbearing a mathematical operator in addition to their number, and motivecells without any mathematical operator in addition to their number. 2.The board game apparatus of claim 1, wherein the mathematical operatorsdefine functions operating on first and second variables, the firstvariable preferably being the number borne on the cell of thatmathematical operator and the second variable preferably being anynumber borne on one of the dice.
 3. The board game apparatus of claim 2,wherein the mathematical operators defining functions operating on firstand second variables include one or more of add, subtract, divide, andmultiply operators.
 4. The board game apparatus of claim 2, wherein themathematical operators defining functions operating on first and secondvariables include one or more of greater than operators and less thanoperators.
 5. The board game apparatus of claim 2, wherein each andevery mathematical operator defining a function operating on first andsecond variables results in a whole number when the first variable isthe number borne on the cell of that mathematical operator and thesecond variable is any number borne on one of the dice.
 6. The boardgame apparatus of claim 5, wherein the whole number is always a numberthat is borne on one of the cells of the board.
 7. The board gameapparatus of claim 1, wherein the mathematical operators definefunctions acting on single variables, the mathematical operatorsdefining functions operating on single variables including one or moreof square and square root operators.
 8. The board game apparatus ofclaim 1, wherein the continuous path along the cells is a spiral thatinwardly spirals from the starting cell at an edge of the board to theending cell at a centre of the board.
 9. The board game apparatus ofclaim 1, wherein the sequential numbering increments the number of eachcell by one compared to the previous cell of the continuous path fromthe starting cell to the ending cell.
 10. The board game apparatus ofclaim 9, wherein the cells comprise 144 cells that are sequentiallynumbered from 1 to
 144. 11. The board game apparatus of claim 1, whereinthe active cells comprise one or more cells bearing one or more of thenumbers 30, 40, 47, 74, 92, 99, 107, 117, 138, and wherein themathematical operators of those cells are addition operators.
 12. Theboard game apparatus of claim 1, wherein the active cells comprise oneor more cells bearing one or more of the numbers 48, 66, 113, 133, 142,and wherein the mathematical operators of those cells are subtractionoperators.
 13. The board game apparatus of claim 1, wherein the activecells comprise one or more cells bearing one or more of the numbers 4,20, 24, and wherein the mathematical operators of those cells aremultiplication operators.
 14. The board game apparatus of claim 1,wherein the active cells comprise one or more cells bearing one or moreof the numbers 60, 120, and wherein the mathematical operators of thosecells are division operators.
 15. The board game apparatus claim 1,wherein the active cells comprise one or more cells bearing one or moreof the numbers 9, 11, and wherein the mathematical operators of thosecells are square operators.
 16. The board game apparatus of claim 1,wherein the active cells comprise one or more cells bearing one or moreof the numbers 36, 64, 100, and wherein the mathematical operators ofthose cells are square root operators.
 17. The board game apparatus ofclaim 1, wherein the mathematical operators comprise square and squareroot operators, and wherein the number of any active cell bearing asquare operator, when squared, does not equal the number of an activecell having a square root operator.
 18. The board game apparatus ofclaim 1, wherein each dice has six faces bearing the numbers 1 to 6respectively.
 19. The board game apparatus of claim 1, wherein the oneor more playing pieces comprise pairs of playing pieces, the playingpieces of each pair being identical to one another.
 20. The board gameapparatus of claim 1, wherein the active cells comprise one or morecells bearing one or more of the numbers 43, 55, 62, 72, and wherein themathematical operators of those cells are greater than operators. 21.The board game apparatus of claim 1, wherein the active cells compriseone or more cells bearing one or more of the numbers 17, 71, 88, 126,136, and wherein the mathematical operators of those cells are less thanoperators.
 22. The board game apparatus of claim 1, wherein a second oneof the active cells is placed a first number of cells along thecontinuous path from a first one of the active cells, wherein the firstnumber is equal to a result of a rolled number applied to themathematical operator borne by the first one of the active cells, andwherein the rolled number is a number which is rollable by one of thedice.
 23. A board game apparatus, comprising a board, one or moreplaying pieces, and one or more dice, wherein the board has a pluralityof cells extending between a starting cell and an ending cell, theplurality of cells being marked with sequential numbers to define acontinuous path along the cells from the starting cell to the endingcell, such that each cell bears a unique number, wherein the cellscomprise active cells each bearing a mathematical operator in additionto their sequential number, and motive cells without any mathematicaloperator in addition to their sequential number, wherein themathematical operators comprise mathematical operators that definefunctions operating on first and second variables, the first variablebeing the sequential number borne on the cell of that mathematicaloperator and the second variable being any number borne on one of thedice, and wherein every one of those mathematical operators definingfunctions operating on first and second variables, when operated withthe sequential number of the cell bearing that mathematical operator,and a number borne on one of the dice, results in one of the sequentialnumbers that is present on one of the cells of the board.